यदि किसी त्रिभुज के कोण 9 ∶ 11 ∶ 16 के अनुपात में हैं, तो सबसे बड़े कोण और सबसे छोटे कोण के बीच का अंतर है:

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  1. 30°
  2. 25°
  3. 40°
  4. 35°

Answer (Detailed Solution Below)

Option 4 : 35°
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दिया गया है:

किसी त्रिभुज के कोण 9 ∶ 11 ∶ 16 के अनुपात में हैं।

प्रयुक्त सूत्र:

त्रिभुज के कोणों का योग = 180º

गणना:

माना कि कोण 9x, 11x और 16x हैं।

कोणों का योग = 9x + 11x + 16x = 180º

⇒ 36x = 180º

⇒ x = 5º

सबसे बड़ा कोण = 16x = 16 × 5º = 80º

सबसे छोटा कोण = 9x = 9 × 5º = 45º

सबसे बड़े कोण और सबसे छोटे कोण के बीच का अंतर = 80º - 45º = 35º

∴ सही उत्तर विकल्प 4 है।

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